Machine learning of atomic dynamics and statistical surface identities in gold nanoparticles

Metal nanoparticles (NPs) exhibit unique properties distinct from their bulk counterparts due to size, shape, surface features, and dynamic behavior. Gold (Au) NPs are particularly interesting, demonstrating catalytic activity despite bulk gold's inertness. This activity, along with surface plasmon resonance (SPR) properties, makes them attractive for catalysis, sensor devices, and biomedical applications. Metals generally exhibit atomic mobility below their melting point, leading to dynamic surface transformations and reconstruction of AEs. This is even more pronounced in NPs due to size-dependent melting temperatures. Understanding the dynamic properties of surface atomic sites and their evolution is crucial for applications like catalysis, where transient active sites play a key role. Experimental techniques offer insights at single-particle or even atomic resolution, but unraveling atomic motion quantitatively is challenging due to structural dispersion, smoothed-out details in ensemble averages, and the absence of individual atom tracking in experimentally-reconstructed models. Computational modeling, particularly molecular dynamics (MD) simulations, coupled with machine learning (ML), offers a powerful tool to overcome these limitations. Previous work using unsupervised clustering and analysis of smooth overlap of atomic positions (SOAP) data from MD simulations has successfully reconstructed the complexity of molecular systems. This study employs a combined bottom-up data-driven and top-down dictionary-based approach to analyze the temperature-dependent properties of Au NPs at the atomic level, resolving their complex dynamics and identifying their statistical identities.

The literature extensively details the unique properties of gold nanoparticles, highlighting their catalytic activity in contrast to bulk gold's inertness [3-6]. The size dependence of melting temperature in gold nanoparticles has been established [1, 24, 25], emphasizing the importance of considering dynamic effects. Experimental techniques such as HAADF-STEM have directly observed atomic motion in Au NPs [5, 26], although quantifying this motion remains a challenge. Computational methods, including MD simulations, have proven effective in studying Au NPs [5, 40-44], but analyzing the resulting high-dimensional data requires sophisticated techniques. Recent advancements in applying ML techniques, particularly using SOAP vectors and clustering, have shown promise in deciphering the structural and dynamical complexity of molecular systems [23, 45-49]. These methods provide a robust framework for classifying materials and extracting data-driven metrics. This study builds upon these existing methods to provide a more comprehensive analysis of Au NP dynamics.

The study uses classical MD simulations to investigate the temperature-dependent properties of Au NPs with icosahedral, decahedral, and octahedral shapes. The simulations employ the Sutton-Chen many-body potential implemented in LAMMPS. The NPs were initially minimized and then subjected to 2 µs of MD simulations at 300 K, 400 K, and 500 K in the canonical ensemble using a Langevin thermostat. SOAP vectors were used as high-dimensional descriptors of the local atomic environment around each atom. A cutoff radius of 4.48 Å was selected to capture information from neighboring atoms. The SOAP vectors were extracted from 1000 frames (sampled every 1 ns from the last 1 µs of each simulation, representing the steady state) to create a high-dimensional dataset. The bottom-up analysis utilized PCA to reduce dimensionality, followed by HDBSCAN* clustering to identify the main AEs populating the NPs. The 300 K simulation data was used to train the clustering algorithm, which was then applied to data from higher temperatures. A top-down analysis was performed by creating a dictionary of SOAP environments from ideal Au NPs (at 0 K) of different shapes and sizes (icosahedra, decahedra, truncated octahedra). This dictionary was used to classify the AEs identified in the MD simulations as either native (typical of the simulated NP's shape) or non-native. The analysis tracked the emergence, annihilation, lifetime, and interconversion of AEs at different temperatures. Transition matrices were generated to quantify the probabilities of AE transitions, allowing for estimation of AE lifetimes and transition rates. Chord diagrams visualized the dynamic interconnections between AEs. The SOAP distance metric was used to assess the similarity of atomic environments and build the dictionary.

The bottom-up analysis revealed distinct AEs corresponding to different structural locations within the icosahedral NP (Ih309): core (Ico), bulk (Bulk), subsurface (SubSurf), five-folded surface sites (5foldedSS), faces (Faces), edges (Edges), vertexes (Vertexes), and concave sites (Concave). PCA and free energy surface (FES) analysis showed that bulk and subsurface AEs were relatively static at 300 K, while surface AEs were more dynamic. The transition matrix indicated significant inter-AE exchange on the surface at 300 K, increasing with temperature. At 500 K, the surface exhibited pre-melting behavior. Tracking individual atoms demonstrated actual atomic diffusion, not just oscillations, even at 300 K. The top-down analysis, using a dictionary of SOAP environments from various NP shapes, classified AEs as native or non-native. The percentage of non-native AEs on the surface increased with temperature. Histograms showed the population of each AE at different temperatures, and chord diagrams visualized the dynamic interconnections between AEs. The transition matrices from the top-down analysis quantified the probabilities and rates of transitions between AEs, enabling the estimation of AE lifetimes. Analysis of decahedral (Dh348) and truncated octahedral (T0309) NPs showed varying degrees of stability and surface dynamics compared to the icosahedral NP. The analysis demonstrated the consistency between bottom-up and top-down approaches despite differences in AE definitions. The study highlighted the importance of considering both native and non-native AEs in understanding NP behavior.

This combined ML approach provides an unprecedented atomistic-level understanding of Au NP dynamics, surpassing the limitations of experimental methods in tracking individual atom motions. The detailed characterization of AE dynamics offers valuable insights into NP properties and behavior under various conditions. The ability to quantify AE lifetimes and interconversion rates is particularly relevant for applications like catalysis, where the residence time of active sites is crucial for reaction efficiency. The study's findings can inform the design of more effective NP-based catalysts by predicting how changes in conditions might affect NP reactivity based on alterations in atomic dynamics and AE lifetimes. The approach's transferability to other metal NP systems and its potential for optimizing NP performance in various applications (catalysis, sensing, biomedicine) broaden its impact.

This study presents a novel combined bottom-up and top-down machine learning approach for analyzing the atomic dynamics of gold nanoparticles. The method provides detailed information on the lifetimes and interconversion rates of atomic environments, offering a comprehensive understanding of NP behavior. This approach has implications for optimizing the performance of nanoparticles in catalysis and other applications. Future work could explore the application of this methodology to other metal nanoparticles, expanding the understanding of their structural-dynamic-property relationships and informing the design of advanced materials.

The study focuses on specific NP shapes and sizes. The results might not be directly generalizable to all NP morphologies or sizes. The employed force field could influence the quantitative aspects of the results, though tests with different force fields showed similar qualitative trends. While the study offers a valuable framework for predicting reactivity, direct experimental validation of the estimated AE lifetimes and transition rates would strengthen the conclusions.